Prove that |sinh y - sinh x| ≤ (cosh a)|y - x|

• May 26th 2010, 11:11 AM
feyomi
Prove that |sinh y - sinh x| ≤ (cosh a)|y - x|
Let a > 0.
Let x ϵ (0,a) and y ϵ (0,a).
Use the fact that cosh is a primitive of sinh to prove that
|sinh y - sinh x| ≤ (cosh a)|y - x|

Thanks very much for any help.
• May 26th 2010, 12:30 PM
Plato
Use the mean value on $\sinh(t)$ on the interval $[x,y]$.
Note that $\cosh(c)\le \cosh(a)$ if $c.